## 1. If the coordinates of a point are (0, -3), it lies on:

### Answer:

### Explanation:

Any point with x-coordinate as 0 lies on the Y-axis.

## 2. The coordinates of the origin are:

### Answer:

### Explanation:

The origin has both x and y coordinates as zero.

## 3. The distance between the points (3,4) and (3,-4) is:

### Answer:

### Explanation:

Since the x-coordinates are the same, the distance is the difference of the y-coordinates, which is 8 units.

## 4. The point equidistant from (2,3), (4,3) and (3,5) is:

### Answer:

### Explanation:

The point equidistant from three given points will be the circumcenter of the triangle formed by those points.

## 5. The point (4,-5) lies in:

### Answer:

### Explanation:

Points with positive x and negative y coordinates lie in the fourth quadrant.

## 6. If a point P has coordinates (-3,4), then its reflection in the X-axis is:

### Answer:

### Explanation:

The reflection in the X-axis changes the sign of the y-coordinate while the x-coordinate remains the same.

## 7. The slope of the line joining the points (2,3) and (4,7) is:

### Answer:

### Explanation:

Slope = (y2 – y1) / (x2 – x1) = (7 – 3) / (4 – 2) = 2.

## 8. If the coordinates of the midpoint of the line segment joining the points (x1, y1) and (x2, y2) are (x,y), then x is:

### Answer:

### Explanation:

The x-coordinate of the midpoint is the average of the x-coordinates of the given points.

## 9. The y-intercept of the line 3x – 4y = 12 is:

### Answer:

### Explanation:

The y-intercept is the y-coordinate of the point where the line intersects the Y-axis (x=0). Setting x=0 in the equation gives y = -3.

## 10. The equation of the X-axis is:

### Answer:

### Explanation:

The X-axis is a horizontal line, so its equation is y = 0.

## 11. Which of the following lines is parallel to the X-axis?

### Answer:

### Explanation:

A line with an equation in the form y = k, where k is a constant, is parallel to the X-axis.

## 12. The distance between the points (-2,3) and (4,-3) using the distance formula is:

### Answer:

### Explanation:

Distance = √[(4+2)^2 + (-3-3)^2] = 7√2 units.

## 13. The coordinates of a point which divides the line segment joining (1,2) and (3,4) internally in the ratio 1:2 are:

### Answer:

### Explanation:

Using the section formula, the point is [(1*2+3*1)/3, (2*2+4*1)/3] = (5/3,8/3).

## 14. Which of the following represents a line perpendicular to 3x – 4y = 12?

### Answer:

### Explanation:

Two lines are perpendicular if the product of their slopes is -1. The slope of 3x – 4y = 12 is 3/4. Hence, a line with slope -4/3 will be perpendicular to it.

## 15. The area of the triangle with vertices (0,0), (0,4) and (3,0) is:

### Answer:

### Explanation:

The triangle is right-angled at the origin. Area = 0.5 x base x height = 0.5 x 4 x 3 = 6 square units.

## 16. The line represented by 2x – y = 0 has a slope of:

### Answer:

### Explanation:

Rearranging the equation to y = mx + c form, y = 2x. Hence, slope m = 2.

## 17. If the point (p,q) lies on the line y = 3x, then:

### Answer:

### Explanation:

For any point on the line y = 3x, the y-coordinate is thrice the x-coordinate.

## 18. Which of the following is the equation of the Y-axis?

### Answer:

### Explanation:

The Y-axis is represented by the vertical line where x = 0.

## 19. The midpoint of the segment joining the points (a,b) and (c,d) is:

### Answer:

### Explanation:

The coordinates of the midpoint are the averages of the x-coordinates and y-coordinates of the endpoints.

## 20. The line y = mx + c passes through the origin if:

### Answer:

### Explanation:

A line passing through the origin will have its y-intercept c = 0.